Precision measurement of the last bound states in H$_2$ and determination of the H + H scattering length
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| Format: | Preprint |
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2025
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| _version_ | 1866915135820398592 |
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| author | Lai, K. -F. Ubachs, W. Beyer, M. |
| author_facet | Lai, K. -F. Ubachs, W. Beyer, M. |
| contents | The binding energies of the five bound rotational levels $J=0-4$ in the highest vibrational level $v=14$ in the X$^1Σ_g^+$ ground electronic state of H$_2$ were measured in a three-step ultraviolet-laser experiment. Two-photon UV-photolysis of H$_2$S produced population in these high-lying bound states, that were subsequently interrogated at high precision via Doppler-free spectroscopy of the F$^1Σ_g^+$ - X$^1Σ_g^+$ system. A third UV-laser was used for detection through auto-ionizing resonances. The experimentally determined binding energies were found to be in excellent agreement with calculations based on non-adiabatic perturbation theory, also including relativistic and quantum electrodynamical contributions. The $s$-wave scattering length of the H + H system is derived from the binding energy of the last bound $J=0$ level via a direct semi-empirical approach, yielding a value of $a_s$ = 0.2724(5) $a_0$, in good agreement with a result from a previously followed theoretical approach. The subtle effect of the $mα^4$ relativity contribution to $a_s$ was found to be significant. In a similar manner a value for the $p$-wave scattering volume is determined via the $J=1$ binding energy yielding $a_p$ = -134.0000(6) $a_0^3$. The binding energy of the last bound state in H$_2$, the ($v=14$, $J=4$) level, is determined at 0.023(4) cm$^{-1}$, in good agreement with calculation. The effect of the hyperfine substructure caused by the two hydrogen atoms at large internuclear separation, giving rise to three distinct dissociation limits, is discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_01877 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Precision measurement of the last bound states in H$_2$ and determination of the H + H scattering length Lai, K. -F. Ubachs, W. Beyer, M. Atomic Physics Chemical Physics The binding energies of the five bound rotational levels $J=0-4$ in the highest vibrational level $v=14$ in the X$^1Σ_g^+$ ground electronic state of H$_2$ were measured in a three-step ultraviolet-laser experiment. Two-photon UV-photolysis of H$_2$S produced population in these high-lying bound states, that were subsequently interrogated at high precision via Doppler-free spectroscopy of the F$^1Σ_g^+$ - X$^1Σ_g^+$ system. A third UV-laser was used for detection through auto-ionizing resonances. The experimentally determined binding energies were found to be in excellent agreement with calculations based on non-adiabatic perturbation theory, also including relativistic and quantum electrodynamical contributions. The $s$-wave scattering length of the H + H system is derived from the binding energy of the last bound $J=0$ level via a direct semi-empirical approach, yielding a value of $a_s$ = 0.2724(5) $a_0$, in good agreement with a result from a previously followed theoretical approach. The subtle effect of the $mα^4$ relativity contribution to $a_s$ was found to be significant. In a similar manner a value for the $p$-wave scattering volume is determined via the $J=1$ binding energy yielding $a_p$ = -134.0000(6) $a_0^3$. The binding energy of the last bound state in H$_2$, the ($v=14$, $J=4$) level, is determined at 0.023(4) cm$^{-1}$, in good agreement with calculation. The effect of the hyperfine substructure caused by the two hydrogen atoms at large internuclear separation, giving rise to three distinct dissociation limits, is discussed. |
| title | Precision measurement of the last bound states in H$_2$ and determination of the H + H scattering length |
| topic | Atomic Physics Chemical Physics |
| url | https://arxiv.org/abs/2502.01877 |